Bayesian Analysis of Stochastic Volatility Models

Jacquier, Éric; Polson, Nicholas G.; Rossi, Peter E.

doi:10.1198/073500102753410408

Cited by 617 publications

(543 citation statements)

References 27 publications

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“…1 In the model, log-volatility belongs to the parametric, first-order autoregressive, AR(1), class of stochastic volatility which can accomodate stationarity as imposed in the literature (Jacquier et al (1994) and Kim et al (1998)) as well as nonstationary deviations from this assumption. The rest of the model is nonparametric in the sense that no assumptions are made about the underlying joint distribution of returns and volatility.…”

Section: Introductionmentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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Section: Introductionmentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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“…For this reason, samplers based on such blocking have appeared in various contexts (e.g., Jacquier et al, 1994;Geweke and Zhou, 1996;Aguilar and West, 2000;Kose et al, 2003;Hogan and Tchernis, 2004). Unfortunately, the MCMC output produced under Scheme 1 often suffers from slow convergence and poor mixing.…”

Section: Dynamic Factor Modelmentioning

confidence: 99%

“…y π η θ A similar approach was also developed by Chib (1996Chib ( , 1998 for hidden Markov models. The sampling techniques have been applied in other settings such as seemingly unrelated regression (SUR) models with serial correlation and time varying parameters (Chib and Greenberg, 1995) and stochastic volatility models (Jacquier et al, 1994;Shephard and Pitt, 1997;Kim et al, 1998). The methods are carefully reviewed in Kim and Nelson (1999) and Durbin and Koopman (2001) and the basic recursions are briefly summarised in Appendix A.…”

Section: Introductionmentioning

confidence: 99%

Efficient simulation and integrated likelihood estimation in state space models

Chan¹,

Jeliazkov²

2009

IJMMNO

229

274

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Abstract:We consider the problem of implementing simple and efficient Markov chain Monte Carlo (MCMC) estimation algorithms for state space models. A conceptually transparent derivation of the posterior distribution of the states is discussed, which also leads to an efficient simulation algorithm that is modular, scalable and widely applicable. We also discuss a simple approach for evaluating the integrated likelihood, defined as the density of the data given the parameters but marginal of the state vector. We show that this high-dimensional integral can be easily evaluated with minimal computational and conceptual difficulty. Two empirical applications in macroeconomics demonstrate that the methods are versatile and computationally undemanding. In one application, involving a time-varying parameter model, we show that the methods allow for efficient handling of large state vectors. In our second application, involving a dynamic factor model, we introduce a new blocking strategy which results in improved MCMC mixing at little cost. The results demonstrate that the framework is simple, flexible and efficient.

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“…That is, the observations are a zero-mean process with time-varying log-variance that one wants to estimate. The SV model is popular in the study of nonlinear state-space models (due to the estimation challenges that it presents [15,[48][49][50]) and is of interest in finance (due to its applicability in the study of stock returns [17,[51][52][53]). …”

Section: Practical Applicationmentioning

confidence: 99%

“…To that end, two classes of problems are contemplated: one where the processes and the observations are linear functions of the states with additive and Gaussian perturbations and another where the functions are nonlinear and/or the noises are not Gaussian. The former class allows for estimating the latent process by optimal methods (e.g., Kalman filtering [16]) while the latter, by resorting to suboptimal methods, based on Bayesian theory [17] or other approximating techniques [18]. Precisely, popular approaches are based on (1) model transformations (e.g., extended Kalman filtering [19]), (2) resorting to QML solutions [15], and (3) Monte Carlo sampling principles.…”

Section: Introductionmentioning

confidence: 99%

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

Urteaga

Bugallo

Djurić

2017

EURASIP J. Adv. Signal Process.

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We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t + 1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

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Bayesian Analysis of Stochastic Volatility Models

Cited by 617 publications

References 27 publications

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Efficient simulation and integrated likelihood estimation in state space models

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

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